Search ETDs:
Rigorous exponential asymptotics for a nonlinear third order difference equation
Liu, Xing

2004, Doctor of Philosophy, Ohio State University, Mathematics.
In the present thesis, we study a particular 3-D map with a parameter ε>0, which has two fixed points. One fixed point has a 1-D unstable manifold, while the other has a 1-D stable manifold. The main result is that we prove the smallest distance between theupdate.cgi two manifolds is exponentially small in ε for small ε. We first prove in the limit of ε → 0+, bounded away from +∞ or -∞, both the stable and unstable manifolds asymptotes to a heteroclinic orbit for a differential equation. Then we show there exists a parameterization of the manifolds so that they differ exponentially in ε. By examining the inner region around the nearest complex singularity of the limiting solution, and using Borel analysis, we relate the constant multiplying the exponentially small term to the Stokes constant of the leading order inner equation.
Saleh Tanveer (Advisor)
Yuan Lou (Other)
FeiRan Tian (Other)

Recommended Citations

Hide/Show APA Citation

Liu, X. (2004). Rigorous exponential asymptotics for a nonlinear third order difference equation. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

Hide/Show MLA Citation

Liu, Xing. "Rigorous exponential asymptotics for a nonlinear third order difference equation." Electronic Thesis or Dissertation. Ohio State University, 2004. OhioLINK Electronic Theses and Dissertations Center. 26 Sep 2017.

Hide/Show Chicago Citation

Liu, Xing "Rigorous exponential asymptotics for a nonlinear third order difference equation." Electronic Thesis or Dissertation. Ohio State University, 2004. https://etd.ohiolink.edu/

Files

osu1101927781.pdf (876.21 KB) View|Download